TAHA Engineering Toolsby TAHA Knowledge Lab

Metrology & Quality

Vernier Caliper Least Count & Reading Calculator

Least count of a vernier scale, and the reading with zero-error correction.

Inputs

Calculate from
A main scale with millimetre ticks above a sliding vernier scale whose seventh line lines up with a main-scale line.203040010coinciding linevernier scalemain scale above
Main scale (top) and vernier scale (bottom). The vernier divisions are slightly shorter than the main-scale divisions; read the main scale before the vernier zero, then add the number of the vernier line that lines up exactly (highlighted) × least count. Diagram not to scale.

Common: one fewer than the vernier divisions (49 for a 50-division vernier). Extended scales cover 2N − 1 (e.g. 39 for 20 divisions).

Result

Least count (smallest reading)
0.02
Value of one vernier division
0.98
Working
1 vernier division = 49 × 1 ÷ 50 = 0.98 mm Least count = 1 − 0.98 = 0.02 mm (= 1 ÷ 50)

This vernier can be read to 0.02 mm.

Educational estimate — check the assumptions below.

About this calculator

A vernier caliper reads finer than its main scale by using a second, sliding vernier scale whose divisions are slightly shorter than the main-scale divisions. The least count — the smallest change the instrument can show — is the difference between a main-scale division and a vernier division. This calculator finds the least count from the scale layout, and combines the main-scale reading, the coinciding vernier line and any zero error into a final reading.

Formula

1 VSD = (m × s) ÷ N    Least count = s − 1 VSD = s ÷ N (for m = N − 1)

Reading = MSR + (k × LC) − zero error

s = value of one main scale division, N = number of vernier divisions, m = main scale divisions covered by those N vernier divisions, VSD = vernier scale division, MSR = main scale reading, k = number of the vernier line that lines up with a main-scale line. A positive zero error is subtracted.

Worked example

  • Main scale 1 mm, 50 vernier divisions covering 49 mm: 1 VSD = 0.98 mm; least count = 1 − 0.98 = 0.02 mm.
  • Reading: MSR 24 mm, 17th vernier line coincides, zero error +0.04 mm → 24 + 17 × 0.02 − 0.04 = 24.30 mm.
  • Inch caliper: main scale 0.025 in, 25 vernier divisions covering 24 → least count 0.001 in.
  • Extended vernier: 20 divisions over 39 mm → 1 VSD = 1.95 mm; least count = 2 − 1.95 = 0.05 mm.

Assumptions and limitations

  • The least count is the reading resolution of the scale, not the accuracy of the instrument. Accuracy also depends on calibration, jaw wear, alignment, measuring force and temperature.
  • Dial and digital calipers show the reading directly; their resolution is stated on the instrument.
  • Zero error sign convention: positive when the instrument reads above zero with the jaws closed. Correction = − zero error.

References

  • Vernier principle and least count (standard metrology texts).
  • ISO 13385-1: calipers — design and metrological characteristics.